Can hypothyroidism cause false negative HPT?

I read somewhere that this can happen to those with hypothyroidism. My husband and I have been TTC for 18 months with no luck due to no periods happening on my own. My PCP just found I have a "slight hypothyroidism" and put me on 25mcg of Levothyroxine. My cousin moved in with us early this month and she swears something is up because her body is doing weird things despite being on the pill. We've both had a total lack of energy, frequent headaches/migraines, and bloating (and extreme gas for me). I've also had increased sex drive, bleeding gums, and my husband tells me that I "smell different" downstairs. Lol! I have an appointment to see my OBGYN on November 15, but I've taken hpt twice in the last two weeks (the last one a week ago) and they were negative. I'm currently on cycle day 61, but I've gone as long as 173 before a period.  Any clues?